Semisimple extensions and elements of trace 1

DOI10.1016/0021-8693(92)90025-HzbMath0788.16029OpenAlexW1994202792MaRDI QIDQ1194045

Miriam Cohen, Davida Fischman

Publication date: 27 September 1992

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(92)90025-h

zbMATH Keywords

Hopf algebrasseparabilitysurjectivityextensionsmash productsMorita contextsemisimple extensionstructure map\(H\)-Galois extensionbimodule direct summand

Mathematics Subject Classification ID

Related Items (24)

Morita theory for corings and cleft entwining structures. ⋮ Unnamed Item ⋮ Semiinvariants for Hopf algebra actions ⋮ A Maschke type theorem for Doi-Hopf modules and applications ⋮ Hochschild cohomology on Hopf Galois extensions ⋮ Braided module and comodule algebras, Galois extensions and elements of trace 1. ⋮ On Hopf Galois extension of separable algebras ⋮ Galois extensions for co-Frobenius Hopf algebras ⋮ Morita, Galois, and the trace map: a survey ⋮ Induction functors and stable Clifford theory for Hopf modules ⋮ Separable extensions for crossed products over monoidal Hom-Hopf algebras ⋮ Frobenius cowreaths and Morita contexts ⋮ Crossed coproducts and cleft coextensions ⋮ On weak crossed products of weak Hopf algebras. ⋮ A Hopf algebra having a separable Galois extension is finite dimensional ⋮ On Frobenius and separable Galois cowreaths ⋮ Integrals in Hopf Algebras over Rings ⋮ Subrings of invariants for actions of finite-dimensional Hopf algebras ⋮ Morita Contexts, π-Galois Extensions for Hopf π-Coalgebras ⋮ Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties ⋮ Separable functors for the category of Doi-Hopf modules, applications ⋮ Cosemisimple coextensions and homological dimension of smash coproducts. ⋮ A co-Frobenius Hopf algebra with a separable Galois extension is finite ⋮ The semisimplicity of smash products of quantum commutative algebras

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• Hopf Galois extensions, smash products, and Morita equivalence
• Hopf algebra actions
• Hopf-Galois extensions of algebras, the Miyashita-Ulbrich action, and Azumaya algebras
• Crossed products and Galois extensions of Hopf algebras
• Minimal quasitriangular Hopf algebras
• On semisimple extensions and separable extensions over non commutative rings
• When Hopf algebras are Frobenius algebras
• Hopf algebra constructions and representation theory
• Crossed Products and Inner Actions of Hopf Algebras
• A Hopf Algebra Freeness Theorem
• Galoiserweiterungen von night-kommutativen ringen

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